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<span class="kw">let </span><font color="Maroon" title="c1">FCPS</font> be   <a href="anproj_2.html#NV10" title="ANPROJ_2:NV.10">up-3-dimensional</a>  <a href="anproj_2.html#NM1" title="ANPROJ_2:NM.1">CollProjectiveSpace</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font>, <font color="Olive" title="b3">c</font>, <font color="Olive" title="b4">o</font>, <font color="Olive" title="b5">d</font>, <font color="Olive" title="b6">d9</font>, <font color="Olive" title="b7">a9</font>, <font color="Olive" title="b8">b9</font>, <font color="Olive" title="b9">s</font>, <font color="Olive" title="b10">t</font>, <font color="Olive" title="b11">u</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">FCPS</font>  st <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>,<font color="Olive" title="b3">c</font>,<font color="Olive" title="b4">o</font> <a href="projdes1.html#R1" title="PROJDES1:pred.1">are_coplanar</a>  &amp;  not <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>,<font color="Olive" title="b3">c</font>,<font color="Olive" title="b5">d</font> <a href="projdes1.html#R1" title="PROJDES1:pred.1">are_coplanar</a>  &amp;  not <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>,<font color="Olive" title="b5">d</font>,<font color="Olive" title="b4">o</font> <a href="projdes1.html#R1" title="PROJDES1:pred.1">are_coplanar</a>  &amp; <font color="Olive" title="b4">o</font>,<font color="Olive" title="b5">d</font>,<font color="Olive" title="b6">d9</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  &amp; <font color="Olive" title="b4">o</font>,<font color="Olive" title="b1">a</font>,<font color="Olive" title="b7">a9</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  &amp; <font color="Olive" title="b4">o</font>,<font color="Olive" title="b2">b</font>,<font color="Olive" title="b8">b9</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  &amp; <font color="Olive" title="b1">a</font>,<font color="Olive" title="b5">d</font>,<font color="Olive" title="b9">s</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  &amp; <font color="Olive" title="b7">a9</font>,<font color="Olive" title="b6">d9</font>,<font color="Olive" title="b9">s</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  &amp; <font color="Olive" title="b2">b</font>,<font color="Olive" title="b5">d</font>,<font color="Olive" title="b10">t</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  &amp; <font color="Olive" title="b8">b9</font>,<font color="Olive" title="b6">d9</font>,<font color="Olive" title="b10">t</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  &amp; <font color="Olive" title="b3">c</font>,<font color="Olive" title="b5">d</font>,<font color="Olive" title="b11">u</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  &amp; <font color="Olive" title="b4">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b7">a9</font> &amp; <font color="Olive" title="b5">d</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b6">d9</font> &amp; <font color="Olive" title="b4">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b8">b9</font> holds <br/> not <font color="Olive" title="b9">s</font>,<font color="Olive" title="b10">t</font>,<font color="Olive" title="b11">u</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c2">a</font>, <font color="Maroon" title="c3">b</font>, <font color="Maroon" title="c4">c</font>, <font color="Maroon" title="c5">o</font>, <font color="Maroon" title="c6">d</font>, <font color="Maroon" title="c7">d9</font>, <font color="Maroon" title="c8">a9</font>, <font color="Maroon" title="c9">b9</font>, <font color="Maroon" title="c10">s</font>, <font color="Maroon" title="c11">t</font>, <font color="Maroon" title="c12">u</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">FCPS</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c5">o</font> <a href="projdes1.html#R1" title="PROJDES1:pred.1">are_coplanar</a>  &amp;  not <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c6">d</font> <a href="projdes1.html#R1" title="PROJDES1:pred.1">are_coplanar</a>  &amp;  not <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c6">d</font>,<font color="Maroon" title="c5">o</font> <a href="projdes1.html#R1" title="PROJDES1:pred.1">are_coplanar</a>  &amp; <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c6">d</font>,<font color="Maroon" title="c7">d9</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  &amp; <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c8">a9</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  &amp; <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c9">b9</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  &amp; <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c6">d</font>,<font color="Maroon" title="c10">s</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  &amp; <font color="Maroon" title="c8">a9</font>,<font color="Maroon" title="c7">d9</font>,<font color="Maroon" title="c10">s</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  &amp; <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c6">d</font>,<font color="Maroon" title="c11">t</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  &amp; <font color="Maroon" title="c9">b9</font>,<font color="Maroon" title="c7">d9</font>,<font color="Maroon" title="c11">t</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  &amp; <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c6">d</font>,<font color="Maroon" title="c12">u</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  &amp; <font color="Maroon" title="c5">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c8">a9</font> &amp; <font color="Maroon" title="c6">d</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c7">d9</font> &amp; <font color="Maroon" title="c5">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c9">b9</font> implies  not <font color="Maroon" title="c10">s</font>,<font color="Maroon" title="c11">t</font>,<font color="Maroon" title="c12">u</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  )</span><br/>























<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:27"/><span class="lab"><font color="Green" title="E23">A1</font></span>: 
<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c5">o</font> <a href="projdes1.html#R1" title="PROJDES1:pred.1">are_coplanar</a> 
 <span class="kw">and </span><br/><a NAME="E2:27"/><span class="lab"><font color="Green" title="E24">A2</font></span>: 
 not <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c6">d</font> <a href="projdes1.html#R1" title="PROJDES1:pred.1">are_coplanar</a> 
 <span class="kw">and </span><br/><a NAME="E3:27"/><span class="lab"><font color="Green" title="E25">A3</font></span>: 
 not <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c6">d</font>,<font color="Maroon" title="c5">o</font> <a href="projdes1.html#R1" title="PROJDES1:pred.1">are_coplanar</a> 
 <span class="kw">and </span><br/><a NAME="E4:27"/><span class="lab"><font color="Green" title="E26">A4</font></span>: 
<font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c6">d</font>,<font color="Maroon" title="c7">d9</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a> 
 <span class="kw">and </span><br/><a NAME="E5:27"/><span class="lab"><font color="Green" title="E27">A5</font></span>: 
<font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c8">a9</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a> 
 <span class="kw">and </span><br/><a NAME="E6:27"/><span class="lab"><font color="Green" title="E28">A6</font></span>: 
<font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c9">b9</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a> 
 <span class="kw">and </span><br/><a NAME="E7:27"/><span class="lab"><font color="Green" title="E29">A7</font></span>: 
<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c6">d</font>,<font color="Maroon" title="c10">s</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a> 
 <span class="kw">and </span><br/><a NAME="E8:27"/><span class="lab"><font color="Green" title="E30">A8</font></span>: 
<font color="Maroon" title="c8">a9</font>,<font color="Maroon" title="c7">d9</font>,<font color="Maroon" title="c10">s</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a> 
 <span class="kw">and </span><br/><a NAME="E9:27"/><span class="lab"><font color="Green" title="E31">A9</font></span>: 
<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c6">d</font>,<font color="Maroon" title="c11">t</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a> 
 <span class="kw">and </span><br/><a NAME="E10:27"/><span class="lab"><font color="Green" title="E32">A10</font></span>: 
<font color="Maroon" title="c9">b9</font>,<font color="Maroon" title="c7">d9</font>,<font color="Maroon" title="c11">t</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a> 
 <span class="kw">and </span><br/><a NAME="E11:27"/><span class="lab"><font color="Green" title="E33">A11</font></span>: 
<font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c6">d</font>,<font color="Maroon" title="c12">u</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a> 
 <span class="kw">and </span><br/><a NAME="E12:27"/><span class="lab"><font color="Green" title="E34">A12</font></span>: 
<font color="Maroon" title="c5">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c8">a9</font>
 <span class="kw">and </span><br/><a NAME="E13:27"/><span class="lab"><font color="Green" title="E35">A13</font></span>: 
<font color="Maroon" title="c6">d</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c7">d9</font>
 <span class="kw">and </span><br/><a NAME="E14:27"/><span class="lab"><font color="Green" title="E36">A14</font></span>: 
<font color="Maroon" title="c5">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c9">b9</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  not <font color="Maroon" title="c10">s</font>,<font color="Maroon" title="c11">t</font>,<font color="Maroon" title="c12">u</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a> </span><br/>

<a NAME="E15:27"/><span class="lab"><font color="Green" title="E37">A15</font></span>: 
<font color="Maroon" title="c6">d</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c3">b</font> <a href="projdes1.html#R1" title="PROJDES1:pred.1">are_coplanar</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="projdes1.html#T14" target="_self" title="PROJDES1:th.14">Th18</a></span>;<br/>
<a NAME="E16:27"/><span class="lab"><font color="Green" title="E38">A16</font></span>: 
 not <font color="Maroon" title="c6">d</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c2">a</font> <a href="projdes1.html#R1" title="PROJDES1:pred.1">are_coplanar</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:27"><span class="lab"><font color="Green" title="E24">A2</font></span></a>, <a class="ref" href="projdes1.html#T7" target="_self" title="PROJDES1:th.7">Th11</a></span>;<br/>
<a NAME="E17:27"/><span class="kw">then </span><span class="lab"><font color="Green" title="E39">A17</font></span>: 
 not <font color="Maroon" title="c6">d</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="projdes1.html#T6" target="_self" title="PROJDES1:th.6">Th10</a></span>;<br/>
<a NAME="E18:27"/>
 not <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c6">d</font>,<font color="Maroon" title="c5">o</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:27"><span class="lab"><font color="Green" title="E25">A3</font></span></a>, <a class="ref" href="projdes1.html#T6" target="_self" title="PROJDES1:th.6">Th10</a></span>;<br/>
<a NAME="E19:27"/><span class="kw">then </span>
 not <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c6">d</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="projdes1.html#T1" target="_self" title="PROJDES1:th.1">Th1</a></span>;<br/>
<a NAME="E20:27"/><span class="kw">then </span><span class="lab"><font color="Green" title="E40">A18</font></span>: 
<font color="Maroon" title="c11">t</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c6">d</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:27"><span class="lab"><font color="Green" title="E26">A4</font></span></a>, <a class="txt" href="#E6:27"><span class="lab"><font color="Green" title="E28">A6</font></span></a>, <a class="txt" href="#E10:27"><span class="lab"><font color="Green" title="E32">A10</font></span></a>, <a class="txt" href="#E13:27"><span class="lab"><font color="Green" title="E35">A13</font></span></a>, <a class="txt" href="#E14:27"><span class="lab"><font color="Green" title="E36">A14</font></span></a>, <a class="ref" href="projdes1.html#T5" target="_self" title="PROJDES1:th.5">Th8</a></span>;<br/>
<a NAME="E21:27"/>
( <font color="Maroon" title="c6">d</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c11">t</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  &amp; <font color="Maroon" title="c6">d</font>,<font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c12">u</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:27"><span class="lab"><font color="Green" title="E31">A9</font></span></a>, <a class="txt" href="#E11:27"><span class="lab"><font color="Green" title="E33">A11</font></span></a>, <a class="ref" href="projdes1.html#T1" target="_self" title="PROJDES1:th.1">Th1</a></span>;<br/>
<a NAME="E22:27"/><span class="kw">then </span><span class="lab"><font color="Green" title="E41">A19</font></span>: 
<font color="Maroon" title="c11">t</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c12">u</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E17:27"><span class="lab"><font color="Green" title="E39">A17</font></span></a>, <a class="txt" href="#E20:27"><span class="lab"><font color="Green" title="E40">A18</font></span></a>, <a class="txt" href="projdes1.html#E6"><span class="lab"><font color="Green" title="E3">Lm1</font></span></a></span>;<br/>
<a NAME="E23:27"/><span class="lab"><font color="Green" title="E42">A20</font></span>: 
<font color="Maroon" title="c6">d</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c6">d</font> <a href="projdes1.html#R1" title="PROJDES1:pred.1">are_coplanar</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="projdes1.html#T14" target="_self" title="PROJDES1:th.14">Th18</a></span>;<br/>
<a NAME="E24:27"/>
 not <font color="Maroon" title="c6">d</font>,<font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c2">a</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:27"><span class="lab"><font color="Green" title="E25">A3</font></span></a>, <a class="ref" href="projdes1.html#T6" target="_self" title="PROJDES1:th.6">Th10</a></span>;<br/>
<a NAME="E25:27"/><span class="kw">then </span>
 not <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c6">d</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="projdes1.html#T1" target="_self" title="PROJDES1:th.1">Th1</a></span>;<br/>
<a NAME="E26:27"/><span class="kw">then </span>
<font color="Maroon" title="c10">s</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c6">d</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:27"><span class="lab"><font color="Green" title="E26">A4</font></span></a>, <a class="txt" href="#E5:27"><span class="lab"><font color="Green" title="E27">A5</font></span></a>, <a class="txt" href="#E8:27"><span class="lab"><font color="Green" title="E30">A8</font></span></a>, <a class="txt" href="#E12:27"><span class="lab"><font color="Green" title="E34">A12</font></span></a>, <a class="txt" href="#E13:27"><span class="lab"><font color="Green" title="E35">A13</font></span></a>, <a class="ref" href="projdes1.html#T5" target="_self" title="PROJDES1:th.5">Th8</a></span>;<br/>
<a NAME="E27:27"/><span class="kw">then </span><span class="lab"><font color="Green" title="E43">A21</font></span>: 
 not <font color="Maroon" title="c6">d</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c10">s</font> <a href="projdes1.html#R1" title="PROJDES1:pred.1">are_coplanar</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:27"><span class="lab"><font color="Green" title="E29">A7</font></span></a>, <a class="txt" href="#E16:27"><span class="lab"><font color="Green" title="E38">A16</font></span></a>, <a class="ref" href="projdes1.html#T15" target="_self" title="PROJDES1:th.15">Th19</a></span>;<br/>
<a NAME="E28:27"/>
<font color="Maroon" title="c3">b</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c6">d</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:27"><span class="lab"><font color="Green" title="E24">A2</font></span></a>, <a class="ref" href="projdes1.html#T14" target="_self" title="PROJDES1:th.14">Th18</a></span>;<br/>
<a NAME="E29:27"/><span class="kw">then </span><span class="lab"><font color="Green" title="E44">A22</font></span>: 
<font color="Maroon" title="c6">d</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c11">t</font> <a href="projdes1.html#R1" title="PROJDES1:pred.1">are_coplanar</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:27"><span class="lab"><font color="Green" title="E31">A9</font></span></a>, <a class="txt" href="#E15:27"><span class="lab"><font color="Green" title="E37">A15</font></span></a>, <a class="txt" href="#E23:27"><span class="lab"><font color="Green" title="E42">A20</font></span></a>, <a class="ref" href="projdes1.html#T10" target="_self" title="PROJDES1:th.10">Th14</a></span>;<br/>
<a NAME="E30:27"/>
<font color="Maroon" title="c6">d</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c4">c</font> <a href="projdes1.html#R1" title="PROJDES1:pred.1">are_coplanar</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="projdes1.html#T14" target="_self" title="PROJDES1:th.14">Th18</a></span>;<br/>
<a NAME="E31:27"/><span class="kw">then </span>
<font color="Maroon" title="c6">d</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c12">u</font> <a href="projdes1.html#R1" title="PROJDES1:pred.1">are_coplanar</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:27"><span class="lab"><font color="Green" title="E23">A1</font></span></a>, <a class="txt" href="#E3:27"><span class="lab"><font color="Green" title="E25">A3</font></span></a>, <a class="txt" href="#E11:27"><span class="lab"><font color="Green" title="E33">A11</font></span></a>, <a class="txt" href="#E23:27"><span class="lab"><font color="Green" title="E42">A20</font></span></a>, <a class="ref" href="projdes1.html#T10" target="_self" title="PROJDES1:th.10">Th14</a></span>;<br/>
<a NAME="E32:27"/><span class="kw">then </span>
 not <font color="Maroon" title="c11">t</font>,<font color="Maroon" title="c12">u</font>,<font color="Maroon" title="c10">s</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E27:27"><span class="lab"><font color="Green" title="E43">A21</font></span></a>, <a class="txt" href="#E29:27"><span class="lab"><font color="Green" title="E44">A22</font></span></a>, <a class="txt" href="#E22:27"><span class="lab"><font color="Green" title="E41">A19</font></span></a>, <a class="ref" href="projdes1.html#T10" target="_self" title="PROJDES1:th.10">Th14</a></span>;<br/>
<span class="kw">hence </span><a NAME="E33:27"/>
 not <font color="Maroon" title="c10">s</font>,<font color="Maroon" title="c11">t</font>,<font color="Maroon" title="c12">u</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="projdes1.html#T1" target="_self" title="PROJDES1:th.1">Th1</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
